Build-up to the match at Tynecastle was dominated by talk that Rodgers had fallen out with his bosses over possible targets, with three weeks to go for clubs north of the border to bring in new recruits.
Speaking to BBC Sport after the 1-0 loss, however, the Ulsterman stressed that he 'loves every minute' at the club and has no intention of quitting.
"I can't go on about players we want in. Of course we want quality players but there's still improvement in this squad, this team, lots of young players so we'll continue to work with and improve them," he said.
"I love my life here. Despite all reports - there's talk of ultimatums with the board - I don't work that way, my communication is very open, so that's certainly not the case.
"And I'd read somewhere else about walking away. I've got three years left on my contract here and I love every day of my life at Celtic. All I want is for us to improve every aspect of the club. It's a disappointing result for us. We'd a good performance in midweek and drew, but you move on in football very quickly."
Celtic return to action on Tuesday evening with a trip to AEK Athens in the second leg of their Champions League third qualifying round tie, which is poised at 1-1.